Multiple input binary adder-subtracters



May 26, 1959 v J. v. BLANKENBAKER ET AL 2,888,202

MULTIPLE INPUT BINARY ADDER-SUBTRACTERS Filed Nov. 25, 1955 3 Sheets-Sheet 1 /Mfs (Zai/HJM Vzw/770,171.94

May 26, 1959 J. v. BLANKENBAKER ETAL 2,888,202

MULTIPLE INPUT BINARY ADDER-SUBTRACTERS 5 Sheets-Sheet 2 .Filed Nov. 25, 1953 .YPNN

Num.

will x IIII IIL May 26, 1959 J. v. BLANKENBAKER vr-:T AL 2,888,202

MULTIPLE INPUT BINARY ADDER-SUBTRACTERS Filed Nov. 25, 1953 5 Sheets-Sheet 3 ROBERT ROYCE JOHNSON INVENTORS BY n ATTRNEY TIME United States Patent() MULTIPLE INPUT BINARY ADDER-SUBTRACTERS John V. Blankenbaker, Albany, Oreg., and Robert Royce Johnson, Pasadena, Calif., assignors, by mesne assignments, to Hughes Aircraft Company, a corporation of Delaware Application November 2S, 1953, Serial No. 394,296

33 Claims. (Cl. 23S-176) This invention relates to multiple input binary addersubtracters and', more particularly', to multiple input binary adder-subtracters wherein a plurality of input signal series respectively representing the binary numbers to be combined in addition or subtraction are translated into a series of sets of weighted signals in a predetermined binary code, the weighted signals being then utilized to define a series of sets of weighted carry signals and a binary result series.

The present invention provides an extension of the principles introduced in copending U.S. patent application, Serial No. 378,116, for Multiple Input Binary- Coded Decimal Adders and Subtracters, by John V. Blankenbaker, filed. September 2, 1953. In the copending application a novel three-input adder is described wherein three input binaryv signal series X1, Aj, and B,- are each received in the order of least significant binary digit signal rst and most significant binary digit signal last, and wherein the corresponding binary digit signals of each series are simultaneously received and added, j representing the binary digit positions in the respective signal series. As is fully explained in the copending application, the input signal series are translated into a series of sets of signals. Fim and F5253 indicating respectively the presence of one or three l-representing binary signals in binary position j of the input signal series, and the presence of two or three l-representing binary signals in binary position j of the input signal series. The binary sum is then formed by effectively adding the signal series Fil-3 to the series FPE-3, the signal series F,- 123 corresponding to the series F12-3 delayed one binary time interval. As indicated in the copending application, a similar technique of binary adding may befutilized for greater numbers of input signals, a four-input adder being specifically described.

According to the present invention any combination of additions and subtractions of multiple binary input signals representing corresponding binary input numbers may be performed in a manner somewhat similar to that described in the copending application. In general, the technique provided by the present invention is to consider or treat each of the input signals as having a significance of either +1 or `-l` depending upon whether the corresponding binary input number is to be added or subtracted. The input signalsk are then translated to a set of intermediate or weighted signals which indicate the aggregate significance of the input signals in accordance with a predetermined binary code. From the set of intermediate signals, carry signals are formed which are combined with the intermediate signals to produce a result signal series indicating the result asa binary output number. Thus each input signal is evaluated or assigned, by an evaluationalor translation circuit, a significance or value of +1 or -l irrespective of the true binary weight of the input signal. Intermediate or evaluational signals '2,888,202 Patented May 26, 1959- ice the techniques provided by the present invention are readily applicable for use in any numbering system ernploying binary digit signals to represent magnitudes or quantities in accordance with a selected code, examples of such systems being conventional binary, binary-coded decimal and binary-coded octal numbering systems. In

order to facilitate a clear and concise description of the present invention, however, it is assumed at the outset that the multiple-input binary adder-subtracter of the present invention is adapted to operate in a conventional binary numbering system. A conventional binary numbering system may be defined as a numbering system wherein a magntiude or quantity is represented by a group of binary digits having weights of powers of 2, each binary digit of the group having a weight double that of the immediately lesser order binary digit and one-half thatof the immediately greater order binary digit. It is further assumed that each binary signal series or group of binary digit signals is received by the multiple-input binary adder-subtracter of the present invention in the order of least significant binary digit signal first and most significant binary digit last. 'I'hus a binary digit signal delayed one binary digit place and represented by la symbol accompanied by a subscript j+1 will have a weight or significance one-half that of a presently received corresponding signal represented by they same symbol but accompanied by the subscript j.

In subtracting la relatively large quantity from a relatively small quantity, the dilerence or result represents a negative quantity. In accordance with the conventions utilized to illustrate the present invention, a negative quantity is represented by its complement expressed in the true binary numbering system.

In a three-input multiple adder-subtracter, according to the present invention, where the operation Xy---Aj-B,L is to be performed, the input signals Xi, Ai, and B, are considered as having a significance or Weight of +1, 1, and -1, respectively, and are translated to the set of intermediate signals Ff2 and Ffll having a significance yor weight of -2 and +1, respectively. The desired binary result is then formed by effectively subtracting the signal F- fz from signal Ffl. A somewhat similar adder-subtracter, according to the invention, is one for performing the operation X,-+A,-B,-; Xi, A,- and Bj being,7 given the weights of +1, +1, and L+1, respectively, and being translated to the set of intermediate or weighted signals F7-+2 and Pfl having weights of +2 and +1. The desired binary result is then Vformulated by subtracting the signal Ff1 from the signal F,- 1+2.

The principles of the present invention may be extended to any number of input signals, one illustration being a four-input adder-subtracter where the operation is performed. In this multiple adder-subtracter the signals F,- 1+2 (Xi, Ai, Bj) and Ffl (X7, Aj, Bi) are formed first and the operation is completed by combining signals F, 1+2, Ffl, and Y, as three input signalsy having the Weights of +1, 1, and 1, respectively.

Where it is desired to perform any of several addition and substraction operations, the Weighted translation functions may be defined so that at least one function is common to all operations. Thus, the weighted signals Ffi'l,

Fi-l, and Ffl'l required for the operation of: Xj-l-Arl-Bi; Xj-I-Aj-Bjg and Xy--Aj-Bi, respectively, may all be delined as the function F,- 1'3 (Xi, Aj, Bj) indicating that one or three of the corresponding il-representing binary variables are present. Thus, any of a combination of binary operations may be performed with a minimum of additional circuit elements being required.

As pointed out in the above-mentioned copending application, binary adders utilizing an addition principle equivalent to the combination addition-subtraction principle of the present invention are particularly useful in multiple input binary-coded decimal adder-subtracters wherein the binary result, whether sum or difference, must be corrected to the desired binary-coded decimal result. In a similar manner the binary multiple adder-subtracters of the present invention are particularly useful in binarycoded decimal operations equivalent to the type of binary operations described above. Several forms of correction circuits suitable for use with the multiple binary addersubtracters of the present invention in binary-coded decimal arithmetic units are described in copending U.S. patent application Serial No. 378,116 for Multiple input Binary-Coded Decimal Adders and Subtractors, by John V. Blankenbaker, filed September 2, 1953.

Accordingly it is an object of the present invention to provide a multiple input binary adder-subtracter wherein any of a plurality of addition or subtraction operations may be performed with a minimum of circuit elements.

Another object is to provide a multiple input binary adder-subtracter which may be utilized efliciently in a binary-coded decimal arithmetic unit, where the combination of binary sums or differences of a plurality of binarycoded decimal input numbers must be corrected to the desired binary-coded decimal result.

A further object is to provide a multiple input binary adder-subtracter wherein a plurality of input signal series respectively representing the binary numbers to be combined in addition or subtraction are translated into a series of sets of weighted signals in a predetermined binary code, the weighted signals being then utilized to define a series of sets of carry signals and the binary result series.

Still another object is to provide a three-input addersubtracter for performing the operation: Xj-Aj-Bj.

Yet a further object is to provide a three-input addersubtracter for performing the operation: Xy--i-Ai-B7-- Yet another object is to provide a four-input addersubtracter for performing the operation: Xj-i-Ai-Bj-Ye The novel features which are believed to be characteristic of the invention, both as to its organization and method of operation, together with further objects and advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings in which several embodiments of the invention are illustrated by way of examples. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a denition of the limits of the invention.

Fig. l is a schematic diagram of a 3-input binary addersubtracter according to the present invention for performing the operation: Xj-Aj-Bj.

Fig. 2 is a schematic diagram of another form of 3-input adder-subtractor according to the present invention for performing the operation: Xj-i-Aj-Bj.

Fig. 3 is a schematic diagram of a 4-input adder-subtracter according to the present invention for performing the operation: Xj-l-Aj-Bj-Yj.

Fig. 4 is a schematic circuit diagram of a direct current trigger circuit and,

Figs. 5 and 5a are a schematic circuit diagram and a voltage wave form chart, respectively, of a typical complementer circuit.

Reference is now made to Fig. 1 wherein there is shown ran adder-subtracter according to the present invention 4 i v for performing the operation: X,-A,-B,. As shown in Fig. l the adder-subtracter comprises three input means A, B, and X producing complementary signal series Ai, Aj; Bj, j; and Xi, X1, respectively corresponding to the binary digits and complements of three binary input numbers A, B, and X. The signals produced by input means A, B, and X are combined in two gating circuits MFH-1); and 10F(-2)j1 to form a series of sets of intermediate or translation signals Fii'l and Fj-z having weights defined in accordance with a predetermined binary code of +1 and -2 respectively, and representing al1 possible aggregate weights of the input signals A, B, and X considered as having a significance or weight of 1, 1, and +1, respectively.

In order to avoid possible confusion, it should be understood at the outset that a binary signal or binary variable represented by a symbol with a bar ('T) over the symbol indicates the complement of the signal or variable. More specifically, a binary signal represented by a symbol with a bar over the symbol is at all times at the opposite voltage level as a signal represented by the same symbol without the bar Thus in accordance with the convention employed herein, a binary 1 digit is represented by a relatively high voltage level signal and a binary 0 digit by a relatively low voltage level signal. Therefore the complements of these signals, represented by a barred symbol, have relatively low voltage levels for binary 1 digits and relatively high voltage levels for binary 0 digits. As a specific example, a binary 1 digit is represented by a relatively high and a relatively low Ai and j signal, respectively.

The signals F,+1 are converted into corresponding complementary signals F1+1 and Fp through a direct-current triggered circuit F(+1)]`. The signals 13j-2 are utilized as rst carry signals Cj1 and are delayed and complemented through a pulse complementer circuit Co and dip-flop F (-2) j-l producing corresponding output signais F7', 1"`2 and j 1'2.

A second carry signal series C,-2 is formed by effectively subtracting the carry series F,- ,12=C, 11 from signals FH; carry series 0,2 being formed through a carry gating circuit 10C2. The carry series C72 is then delayed and complemented producing signals Cj 12, and C, 12 through a flip-Hop C2 controlled by gating circuit 10C2. A result signal series R, is then formed as a function of signal series F,+1, F:- 1'2 and C,- 12 and their corresponding complements in a result-forming matrix 10Rj.

The flip-ops utilized may be conventional Alip-liops having 1 and 0 input circuits such that signals applied separately to the 1 and 0 input circuits set the flip-flop to stable states representing binary 1 and 0, respectively, and the simultaneous application of signals to both input circuits triggers the ip-op or causes it to change stable states.

A typical ip-op circuit of the above class suitable lfor use -in the adder-substracter of Fig. l is fully illustrated and described in detail in U.S. Patent No. 2,644,887 entitled synchronizing Generator, by A. E. Wolfe, Ir., issued July 7, 1953.

As indicated in Fig. 1, clock pulses Cp are applied to complementer Co and gate 1002. The clock or trigger pulses Cp are orderly, equally spaced pulses which are externally generated and applied to the adder-subtracter circuit of Fig. 1, for synchronizing or timing the operation of the flip-flop circuits F(-2)j-1 and C2. Although the stable states assumed by each of the pops F(-2)j-1 and C2 are regulated or controlled by signals generated by a corresponding gating circuit, as above indicated, this is actually accomplished by selectively gating clock pulses Cp to the ip-flop by the corresponding gating circuit, the clock pulse Cp actually triggering the dip-flop. This will become more apparent in the ensuing description.

asse-,aon

Direct-current trigger circuit (F+'1)j may be any of the well-known types of circuitsr used in the electronic art for receiving two-level or binary input signals and producing a reproduction of these input signals on a first output and the complement of the input signals on a second output. A preferred direct-current trigger circuit of this class is illustrated in Fig. 4. A suitable type of complementer circuit Co for providing pulse input signals for the 1 and 0 input circuits of flip-flop F(-2)j-1 in response to an applied voltage-level or binary signal is illustrated in Fig. 5. Before considering in more detail the operation of the adder-subtracter of Fig. 1, and the detailed structure of the gating circuits F(+l)j, 10F(-2)j-1, 10C2, and 10RJ', it is considered advantageous at this time to consider in more detail the structure and operation of the direct-current trigger circuit F(+l)i, and the complementer circuit C0.

Referring to Fig. 4, there is` presented a schematic circuit diagram F(+1)j indicated by broken lines of a preferred embodiment of the direct-current trigger F(+1)]' of Fig. l, for receiving input signals Ff!"1 on an input lead 403 and for producing complementary output signals fl and F7+1 on output leads 404 and 405, respectively. The direct current trigger F(}-1)j includes a first direct current (D.C.) amplifier 400, a second direct current (D.C.) amplifier 401, and a clamping circuit 402, each indicated by broken lines. The first D C. amplifier 400 is responsive to input signals Fftl on lead 403 for Iproducing, output signals F,-+1 on lead 404, signals ftl being the complement of input signals Fftl. The second D.C. amplifier 401 is coupled t'o the first D C. amplifier 400 and responsive to signals ftl produced by D.C. amplifier 400 for developing signals Fftl on output lead 405. The signals F,+1 are signals having the same phase and voltage amplitude but a greater power capacity than the input signals F,+1 input, i.e., are developed from a lower impedance source. Therefore, from a voltage standpoint, output signals F,-+1 on lead 405 are a reproduction of input signals F1+1 on lead 403, and output signals Fffl are complementary signals of input signals Pfl.

The clamping circuit 402 is coupled to the first D.C. amplifier 400 and the second D.C. amplifier 401 for receiving complementary output signals Pfl-1 and Ffll on leads 405 and 404, respectively, and for clamping the voltage level swings of signals Fffl and F7-+1 within the same limits as the voltage level swings of input signals F,-+1.

D.C. amplifier 400 is a conventional direct current amplifier circuit and includes a triode 410, a plate load resistor 412, a biasing battery 411, and an input voltage divider circuit comprised of resistors 413 a-nd 414 in series. The. input signals Ffl'l appearingV on lead 403 are applied to the upper extremity of the voltage divider circuit, the lower extremity of which is connected to ground. The common junction point of resistors 413 and 414 is connected to the control grid 415 of triode 410, thus by the proper choice of resistance values for resistors 413 and 414, the input signals F,+1 on lead 403 may be reduced to convenient voltage level swings for application to control grid 415. The cathode 416 of tube 410 is returned to ground through the biasing battery 411 thus supplying a convenient grid-cathode bias on tube 410. The anode 417 of tube 410 is coupled to a B+ supply through the load resistance 412. The output lead 404 is directly coupled to the anode 417 of ube 410, thus the output signals ftl on lead 404 are developed as the output signals of the D.C. ampliiier 400 developed by the load resistor 412.

D.C. amplifier 401 is substantially identical to D.C. amplifier 400 above described in that signals ffl developed by amplifier 400 on lead 404 are applied to a control grid 420 of a triode tube 421 through an input voltage divider circuit comprised of resistorsv 422 and 423 6 connected in series' between the input leadVv 404 and ground. The cathode of tube 421 is maintained at a potential positive in relation to the control grid 420 by a bias battery 425. The anode of tube 421 is supplied with a B+ supply through a load resistor 424. The output lead 405 is connected directly to the anode of tube 421 and thus signals F,-+1 appearing on lead 405 are developed as the output signals of D.C. amplifier 401.

Direct current amplifiers of the above described class are fully described in Electronics Experimental Techniques, by William C. Elmore and Mathew Sands, published by McGraw-Hill Book Company, Inc., 1949, pages. t0 183.

The clamping circuit 402 includes ay first diode clamp 430 and a second diode clamp 431. Diode clamp 430 is coupled to output lead 404 for clamping output signals B17-+1 within the limits between two direct-current voltage values El and E2 impressed on clamp 430, and diode clamp 431 is coupled to lead 405 for maintaining signals F7-+1 appearing on lead 405 within the same limits in respense to the voltages E1 and E2 impressed thereon. Diode clamp 430 includes av first diode 432 having its anode connected to the voltage E1, and diode 433 having its cathode connected to Voltage E2, the cathode of diode 432 and the anode of diode 433 being connected commonly to the output lead 404. Thus ldiode clamp 430 operates as a clamping circuit for clamping the signals appearing on lead 404 below the amplitude of voltage E1 and above the amplitude of voltage E2. Diodes 434 and 435 of the diode clamp 431 are similarly connected to the voltages El and Ezrand the output lead 405 and similarly clamp signals Fjl appearing on lead 405 below voltage E1 and above voltage E2. Voltages E1 and E2 are chosen to correspond to the upper and lower limits,

respectively, of the binary or two-level voltage input signals F,+1 appearing on lead 403. Clamping circuits of this class are fully discussed in Electronics Experimental Techniques, by William C. Elmore and Mathew Sands, published by McGraw-Hill Book Company, Inc., 1949, pages 114 to 117.

Reference is now made to Fig. 5 wherein there is presented a typical complementer or complementary sig- 'nal generating network circuit 510 adapted for operation as the complementer circuit Co of Fig. 1. The complementary signal generator network 510 is responsivev to binary or two-level voltage control signals applied at a first' input terminal 512 for selectively gating or passing an electrical pulse or clock signal Cp applied at a second input terminal 514 to produce two complementary electrical pulsev output signals at a first output terminal 515 and' a second output terminal 518, respectively. More specically, the complementer circuit 510 is adapted to effectively gate the input clock pulses Cp to the first output terminal 516 when the binary control signals at terminal 512 have a relatively high or l-representing value, and to the Second output terminal 518 when the control signals at terminal 512 have a relatively low or 0-representing value.

Complementary signal generating network 510 includes rst and second electronic gating circuits 520 and 522, respectively, responsive to different predetermined voltage levels of the applied control signal for selectively presenting the applied electrical pulse signal at output terminals 516 and 51S, respectively. First gating circuit 520 includes a pair of unidirectional current devices, such as crystal diodes 524 and 526, the cathode of diode 524 being connected to input terminal 514 and the cathode of diode 526 being connected to control terminal 512. Diodes 524 and 526 have their anodes connected together at a common junction 528 which is connected to output terminal 516. Common junction 52S is also coupled to one terminal B+ of a source of biasingpotential, not shown, by abiasing resistor 530, the other terminal of they source being grounded.

Second gating circuit 522 also includes a pairof serially connected unidirectional current devices, such as crystal diodes 532 and 534, interconnecting common junction 523 with output terminal 518, the cathode of diode 532 being connected to common junction 528 and the anode of diode 534 being connected to output terminal 518. The common junction 536 of diodes 532 and 534 is in turn coupled to input terminal 514 by a capacitor 538 and to one terminal B+ of the source of biasing potential, not shown, by a biasing resistor 540. In a similar manner, diode 534 has its anode coupled to one terminal E2 of a source of biasing potential, not shown, by a biasing resistor 542. The other terminal of each of the sources is connected to ground. The function of the biasing potentials at terminals B+ and E2 and typical values thereof will be described in detail below. For reasons which will become more clearly understood later,y however, it should be stated that the potential appearing at terminal E2 is lower than the potential at terminal B+.

ln operation, input terminal 514 is connected to a source 544- of negative electrical clock pulses Cp to be selectively passed, and control terminal 512 is connected to a variable potential control or binary signal source, such as a squarewave signal source S46 which controls the selectivity f gating circuits 520 and 522. Source 546 may be any suitable source of a signal having alternate relatively high and relatively low voltage levels, such as a conventional voltage state gating matrix. For example in Fig. l, the gating matrix F(2)j-l is substituted for the square wave signal source 546 of Fig. 5.

Referring now to Fig. 5a, there is shown a composite diagram of the waveforms appearing at various points in the complementary signal generating network of Fig. 5. The control signal, generally designated 547, which is applied to control terminal 512 from source 546, includes alternate relatively low and high voltage levels E2 and E1, respectively, the voltage level E2 corresponding substantially to the biasing potential at terminal E2. The negative electrical pulse or clock signal Cp, generally designated 54S, which is applied to input terminal 514 from source 544, has a steady state voltage level which is preferably substantially equal to potential El, the periodically recurring negative pulse excursions of signal 545 lowering the potential of the signal accordingly.

Assume now that signal 547 is initially at its low potential value of E2, as shown at time to in Fig. 2. Under these conditions the signal, generally designated 529, apr pearinglat common junction 52S will be at a voltage level substantially equal to level E2 due to the clamping action of diode 526. In a similar manner, the signal, generally designated as 537 appearing at common junction 536, will have a potential value substantially equal to E2 due to the clamping action of diode 532. Consequently, the potential difference across diode 534 in second gating circuit 522 is substantially zero volts, whereas diode 524 in rst gating circuit 520 is back-biased by substantially the voltage differential between the voltage levels E1 and E2.

Consider now the behavior of complementary signal generating network 510 when signal 54S includes a first negative pulse 545a, the pulse amplitude being equal to or less than the voltage differential between voltage levels E1 and E2. Since the amplitude of pulse 54511 is insufficient to drive the cathode of diode 524 below voltage level E2, it is apparent that diode 524 will remain back-biased. Accordingly, diode 524 will not pass the negative pulse to common junction 528 and hence to output terminal 516.

When negative pulse 545:1 is applied to input terminal .5l/, the potential of common junction 536, heretofore clamped substantially at level E2 by diode 532, will be lowered accordingly, due to the coupling actionof capacitor 53S. It s clear, of course, .that diode 532-wil1 be immediately back-biased for the duration of pulse 54511, since its cathode is held substantially at level E2 due to the clamping action of diode 526, whereas itsl It is clear, however, that diode 534 is now front-biased by the application of pulse 545a since the potential of common junction 536 and hence the cathode of diode 534 is driven below the voltage level E2 by the magnitude of the applied pulse. Accordingly, negative pulse 545a will be passed by diode 534 and will result in a corresponding negative pulse 519i: in the signal, generally designated 519, which appears at output vterminal 51S.

Assume now that signal 547 swings to its relatively high level potential value E1, and that signal 545 is at its steady state level E1. Under these conditions, the potentials at common junctions 528 and 536 also swing to voltage level E1 due to the clamping action of diodes S26 and 532, respectively. Consequently, the potential difference across diode 524 in first gating circuit 520 is substantially zero, whereas diode 534 in second gating circuit 522 is back-biased by substantially the voltage differential between the voltage levels E1 and E2.

Let us now assume that signal 545 includes a negative. pulse S45b, the amplitude of which is equal to or less than the voltage differential between voltage levels E1 and E2. It is immediately clear that diode 524 willrbe. front-biased and will, therefore, pass pulse 545b andv produce a corresponding output pulse 529b in signal 529 appearing at output terminal 516. j

Although pulse 545b is also applied to common junction 536 by coupling capacitor 538, it will be noted that the pulse 5371 appearing in signal 537 does not lower the potential of common junction 536 below potential level E2. Accordingly, diode 534 will remain backbiased and thereby inhibit the applied negative electrical pulse from appearing at output terminal 518.

If signal 547 applied to control terminal 512 of complementary signal generating network 510 again swings to its low potential value of E2 as illustrated in Fig. 2, a negative pulse 545C applied to input terminal 514 will again produce a corresponding negative pulse 519C at output terminal 518 and will be inhibited from appearing in signal 529 at output terminal 516. It is clear, therefore, that complementary signal generating network S10 is responsive to the relatively high and relatively low potential levels of control signal 547 for selectively passing negative electrical pulses applied at input terminal 512 to produce two complementary output signals at output terminals 51,6l and 518, respectively. In other words, an applied electrical pulse signal will be presented at either output terminal 516 or at output terminal 518 depending upon whether control signal 547 is at its relatively high potential value or its relatively low potential value, respectively.

As set forth above, diode S26 and resistor 530 are utilized for clamping common junction 52S vat substantially the instantaneous voltage of control signal 547. However, diode 526 also performs the additional function of inhibiting electrical pulses appearing at junction 528, such as pulse 529b in signal 529, from being applied back into squarewave signal source 546. For example, when electrical pulse 545b is applied at input terminal 514, the potential of common junction 528 drops below its clamped potential level E1 by the voltage amplitude of pulse 529b. Since the potential El is being applied to the cathode of diode 526 at this time, diode 526 is back-biased for the duration of pulse 529b, thereby effectively isolating source 546 from clock pulse source 544. The combination of diode 526 and resistor 530 may, therefore, be termed an isolating network.

It will be recognized byk those-skilled in the computer art that if squarewave signal source 546 comprisesa voltage state gating matrix having a conventional diode and gate output circuit, the isolating network including diode 526 and resistor 530 may be eliminated from complementary signal generating network 510. In other words, if squarewave signal source 546 includes an and gate output circuit, the function of diode 526 and resistor 530 may be performed by the output circuit of the source, and the isolating network may be excluded from complementary signal generating network 510.

The above described complementer or complementary signal generator is fully described and claimed in copending U.S. patent application, Serial No. 308,045, for

Complementary Signal Generating Network, by Daniel L. Curtis, led September 5, 1952, now Patent No. 2,812,451.

The structure of certain gating circuits such as F( +1) j, 10C2, and 10Rj is defined according to certain Boolean ralgebraic equations which specify the sequences of stable states of the corresponding liip-liops and trigger circuit. Logical Boolean algebraic equations will be frequently employed in this discussion for expressing variables as well as explaining the mechanization of certain gating circuits employing logica and and or circuits or gates which correspond directly to symbols of the logical equations. The logical and and or circuits and their correspondence to symbols utilized in the logical equations are explained in appropriate sections of the ensuing description. Before consideringV the specific mechanization of the gating circuits, therefore, it is essential, for a complete understanding of the invention, to consider the basic algebraic equations delining them. It will be noted that the variables used in the following equations correspond to the electrical signals indicated in Fig. 1, so that each equation may be considered to define an electrical function of the corresponding gating circuit. After the derivation of each equation is completed the equation is given a number corresponding to the gating circuit which it defined. Equation 10F(-l-1)j for example, defines gating circuit 10F(+1)j.

In performing the operation X1-A1-B1 it is apparent that the range of the aggregate weight of the input variables without carries being considered is (-2) through +1. The -aggregate weight (-2) occurs in any place if binary digits A1 and B1 are l 4and X1 is 0, and the weight +1 occurs when X1 is l and both A1 and B1 are 0. 'I'his range may be represented by two signals F1"2 and F1+1 having Weights of -2 and +1 so that the aggregate Weight -2 is indicated by a l-representing signal F12 andl a O-represen'ting signal F1+1g and the aggregate weight {-l is indicated by a O-representing signal F1-'2 and a l-representing signal F1+1. ln a similar manner, the signals F1-2 and F1+1 may be defined to represent any of the other input conditions of signals A1, B1, and X1- as indicated in Table I wherein all eight possible input conditions are considered:

`10 As indicated in Table I, thev variable F1+1 has a 1-representing value whenever one or three of variables`X1, A1, and B1 have l-representing values sothat it may be defined by the function:

where the dot is the logical and and the plus the logical, inclusive on Ity should be noted in .reference to the above logical expression or function for F1+1 that a l-representing value in the table is indicated in the logical expression by thev corresponding symbol of the variable whereas a O-representing value in the table is represented by a bar over the corresponding variable symbol. This in consistent with the previously explained significance of the bar (r) as identifying the complement of a binary variable or signal. Thus when the complement of a variable, as indicated by the bar has a l-representing value, it follows that the corresponding variable will have a O-representing value. This practice isconsistently carried out in the remainder of this description, ie., a O-representing value of a variable being represented in the associated logical expressions by a symbol superimposed by a bar (r'). Since the function F13 (A1, B1, X1) appears frequently in considering the embodiments of the invention it is often convenient to utilize it in the place of its equivalent variable F1+1. For simplicity this function may be represented as F11'3 where it is implied that it is a function of the input signals. The function G13 will be utilized to express a one or three function of other functions, and may be identified simply as the variable G113.

In a similar manner the variable F12 is found, from Table l, to have a l-representing value whenever X1- is O and either A1- or B1 is 1, or when Both A1 and B1 are 1. This relationship is expressed by the function:

wherev the parentheses indicate the logical and function.

The complete weight of the result in any digit position may be represented by variables F12 and F1+1 defined above, and two carry variables C1 11 and C1 12 having Weights of -1 each. It is apparent that the carry signals C1 11 and C1 12 each represented a weight of -2 in the corresponding (j-l)st binary digital place. The binary place representation j-l is utilized to indicate that the carry variables are brought over from the result in the (]'1)st place, where the (j-l)st place is the immediately preceding or next lower order binary place as correspond to the (j) th place. It is apparent from the foregoing description that the carry Variables C1- 11 and C1- 12 correspond to carries C11 and C12 delayed one binary digit time interval. These variables provide sixteen possibilities of results ranging in weight from 4, corresponding to the situation when X1 is 0 and each of the variables A1, B1, C1 12, and C1 11 are 1, to a weight of +1 corresponding to the situation when X1 is 1 and all of the variables A1, B1, C1 12, and C1 11 are 0. A complete set of situations is illustrated in Table II below. Table II also illustrates one manner of defining the translation from signal set F14-2, F1, C1 12, and C1 11 to the set C12, and C11, and R1 corresponding to the nal result and carry digitsv desired.

llll

Table II v Aggregate Weight -2 +1 -l -1 -2 -2 +1 2 .x-Ain,-C,? ,C 1 5? Fr* C} 0,1, C; C, R.

(-4) 1 o 1 1 1 1 o 1 o o 1 1 1 1 (-3) 1 o 1 o 1 1 1 1 1 1 1 1 1 1 0 o 1 1 o 1 0 2 1 0 0 o 1 o 0 1 1 o 1 1 o o 1 1 1 o 1 o o 0 o o 1 o 1 1 1 o o 1 0 o 1 1 o 1 1 1 o 1 1 1 1 o o 1 o 1 o o o 0 o o o (o) 0 1 o 1 o o o o 1 1 o o o u (+1) o 1 o o o o 1 As indicated in Table II the carry variable Cal has been defined as equal to the variable F,"2 so that the carry over signal C, 11 is obtained merely by delaying the signal 11j-2 one binary digit time interval. Reference to Fig. 1 shows that the delay is achieved by entering signal F7-2 through complementer circuit Co into the ip-op for producing corresponding complementary signals F, 12 and F,- 12 after the desired binary digit delay.

From Table II above, a logical Boolean expression for the variable C,2 in terms of the variables C142, Fi', and C51 may be derived in the following manner. It is first determined from the table under what condition the variable C,2 and C, 12 are both 1 value variables. This condition occurs when C,- 12=1 and either F7+1 has a 0 value or C,- 11 has a 1 value, which may be logically expressed as C,2=C,- 12.(17",-+1l-C,- 11). Secondly, those conditions where Cj2 has a 1 value and C7- 12 has a 0 value are noted in the table. This condition occurs when F7+1 has a 0 value and C, 11 simultaneously has a 1 value. This may be expressed as C12=, 12.(F,+1.C,- 11). By logically adding the above two expressions for C72, a combined expression Covering all possibilities of Table II is obtained as follows:

0?:C? ,.(F;L1+C} ,.;f1.c} where both the dot and parenthesis indicate a logical and function, and the plus (-1-) indicates a logical or function in the above expressions.

By substituting the expressions 17171-3 and F, 12 for their equivalence E17-+1 and C,- 11, respectively, in the above expression, the following logical equation is obtained:

variable Ri in terms of the variables C,- 12, Cd 11, and F7-+1 is obtained, thus:

F(2)i-1, and C2, respectively, it is convenient to understand the general form of equations utilized to detine the input signals for ip-flops. The discussion here is brief since the general theory of ilip-op control functions is discussed in considerable detail in copending U.S. patent applications: Serial No. 327,567 for Binary- Coded Flip-Flop Counters, by E. C. Nelson, led December 20, 1952; and Serial No. 327,131 for Binary- Coded Flip-Flop Counters, by R. R. Johnson, iiled December 20, 1952.

There are several types of input functions which may be employed to control an associated flip-flop, four general types of which will be herein discussed. According to one type of equation, the sequence of stable states of the controlled device are directly defined so rthat the value of the equation (l or 0) at a particular time indicates the desired setting of the flip-flop. Where a flipflop circuit is controlled with this type of function it may be set through a complementer circuit such as the complementer Circuit Co previously described. It is convenient to refer to the function defining directly the setting of a ip-op as a setting function. The complementer circuit is utilized to provide a pair of complementary control signals which are applied to the 1 and 0 input circuits, respectively, of the controlled flip-flop. In controlling ip-flops through gating circuits defined by setting functions it will be noted that a one digit time delay is introduced; that is, the ip-flop assumes a stable state during the following digit time interval corresponding to the setting function of the previous time interval.

The complementer circuit is utilized to provide a complementary pair of ip-op control signals in response to applied clock or trigger pulses Cp and applied voltagelevel signals defined by the corresponding setting function. As is evident from the previous discussion of the complementer circuit Co, the impressed clock pulses appear on a lirst output lead only when the impressed voltage-level signals are relatively high and appear on a second output lead when the impressed voltage-level signals are relatively low. Thus by applying the signals from the rst and second output of the complementer on the 1 and 0 input circuits, respectively, of the associated flip-op, the hip-flop is set to stable states corresponding directly to the relative value of the impressed voltagelevel signals. It follows, therefore, that a function, i.e., the setting function, which defines directly the value or relative voltage of the impressed voltage-level signal directly delines the resulting state of the corresponding controlled flip-flop.

According to a second type of defining equation herein referred to as a changing function, the conditions for changing the flip-flop stable state, or triggering the flipop are established. The term triggering is here used to indicate the transfer of the p-op from its existing stable state to its opposite stable state. This is accomplished by simultaneously applying clock pulses to both the 1 and O input of the flip-flop. Thus a changing function denes the conditions for simultaneously applying a clock pulse Cp to both the 1 and the O input of the associated ip-op.

In many situations, it is` desirable to separate the changing type of `equation into two partial-changing functions which separately deline the conditions for changing the associated ip-flop stable state from 0 to 1, and from 1 to 0. The partial-changing functions are particularly useful Where the equations include the output signals of the ip-op to be controlled. In this case the partialchanging functions may be simplified to simplified partial changing functions according to rules which are briefly considered below and fully described in the abovementioned copending applications by E. C. Nelson and R. R. Johnson.

Any convenient notational system may be employed for designating the setting, changing partial chang-v ing, and simplified partial changing functions above by the letter a, b,

defined. For example, in the above-mentioned copending applications by R. R. Johnson and E. C. Nelson, the setting functions are designated by the letter S followed or n indicating the particular Hip-flop which is controlled, and either a 1 or Oldepending upon whether the controlled flp-op is to be set t the 1 or the 0 state, respectively. The changing functions are represented by the letter C followed by the letter a, b, or n, and the partial changing functions are represented in the same manner as the changing functions with the addition of a 1 or `0 indicating whether the flip-flop is changed to 1 or changed to 0. The simplilied partial changing functions are designated by the number 1 or 0 indicating whether the functions define signals applied to the 1 or 0 input of the flip-flop, followed by the letter A, B, or N representing the flip-dop controlled.

Herein the setting function is designated-by the symbol to followed by the alphabetic letters or symbols identifying the Hip-flop controlled. The simplified partial changing functions are identified in a manner similar to that employed in the above-cited copending application to ohnson and Nelson, i.e., by the number l or 0 indicating whether the function defines signals applied to the 1 or 0 input of the ilip-liop, followed by the letter or symbols representing the flip-flop controlled. Thus the setting function for setting a ip-ilop F1 is designated by the notation toF,-, and the simplified partial changing functions as 1F,- and 0l-T, for application to the v1 and 0 input circuits, respectively, of the flip-flop. No notational system is employed herein for changing and partial changing functions as these functions are not employed in this description.

As is more fully explained in the above-mentioned copending applications to E. C. Nelson and R. R..Johnson, any flip-flop function may setting function as follows:

where complementary signals Ff and F7 are produced by be written in the formof a;

a flip-flop Fi, and where G and H may be any' function of variables other than signals Fi and F7. y

The above general setting function may be reduced to the simplified partial changing functions:

functions may be better understood if the nature'I ofthe general setting function is analyzed. One method of analysis is to consider the setting function as defining `the.

conditions for setting the corresponding flip-Hop to its 1'or true state. Under this assumption, the above general setting function expresses the following: (1) if the ilip flop is in the true state, it will be permitted to remain in'. the true or 1 state so long as the function H is equal to 0, i.e., :1; (2) if the ip-op is in the false or 0 state; it

will be triggered to the true or 1 state if the function G is equal to l; and (3) if both the functions G and H are equal to 1 (G=1, H=1), the Hip-flop will be triggered from its present state to its opposite state irrespective of its present state.

It is evident, therefore,1that any setting function expressed in the above general setting function manner may be readily reduced to the corresponding simplified par# tial changing functions by determining the corresponding G and H functions of the setting functions. K

Since the carry function Cjz is to be entered into the flip-flop C2, shown in Fig. 1, it is apparent that the above Expression 3 for C72 may be written in the form of a setting function for flip-flop C2 as: v

weet-autumnmatratze l 14 Iwhich reduces to the simplified partial changing functions:

1G2=",13.F,121 A 0C2=}'34-F, 21

Similarly a setting function for ip-op F(2) j-f1 may be written directly from the above Expression 2 for Ffz as:

where the functions 1C2 and 0C2 respectively indicate the signals applied to the 1 and 0 input circuits of'ipllop C2. The derivation of this carry function isv fully described in copending U.S. patent application Serial No. 1.89318 for Arithmetic Units for Digital Computers, by Eldred C. Nelson, filed October 10, 1950.

Mechanization functions for gates NFH-1);' and lilRj may be obtained directly from the above expres sionsfor F,+1 (Equation 1) and Ry' (Equation 4), thus providing the following complete set of mechanization functions respectively defining gating circuits 10F (+1) i, 10F(2)j-1, 10C2, and 10Rj:

1,3 "-2 Fi -Fi-i (lORj) R,=Ft3F`.-121?1+'Fl'3-FL21-i-1 +F',3.,121.C? 1+F}:3.F;21.C 1 where clock pulses Cp are introduced as a= final and condition to trigger the flip-flop as above explained and to synchronize the entry of digits into the ip-ops, one pulse Cp being applied each binary digit time of operation. No clock pulse is required to control direct-current trigger circuit F(|1)]'. It should be noted that the above Expression 4 for Rj was expanded by well known principles of logical Boolean algebra to produce a mechanization function without parenthetical terms. This is done to provide a simpler gating circuit for 10Rj.

As indicated in Fig. f1, each of the and functions in the equations defining the gating circuits is providedby an and circuit, symbolically represented in the ligure by a semicircle containing a dot D), which responds to signals applied to separate input terminals and produces a l-representing output signal only when all input signals are l-representing signals. Thus, an circuits lRj-l, 10Ri-2, 10Rj-3, and'10Rj-4 provide signals corresponding to the and functions:

Fi'3- i -21-C1g1 Fil'a-Fi-zi-Cag-r respectively, in response to the signal sets: Fi'sr F1121 Cta-13 Fi'a: Far-2r Eli-1; Fi'a, F1121, Gag-1;

Fija: Fai-217 cfg-1; Fina: Fi--zh C12-'1 respectively, each signal being applied to a separate and circuit input terminal. Each of the or functions in the above functions is provided by an or circuit, symbolically represented in the figure by a semicircle containing a plus (E), such as circuit lRj-S shown in Fig. 1 which responds to the and signals produced by circuits 10Rj-l, 10Rj-2, 10Rj-3, and 10Rj-4 and produces a signal corresponding to the function R1'. The mechanization of the other functions should be apparent from this example.

And7 and or circuits are now well-known in the computer art and therefore it is no t deemed necessary "115 16 amples of such circuits are shown on pages37 to v45 of Table IV Hlgh Speed Computing Devices by Engineering Research Associates, published in 1950 by McGraw-Hill v Book Company, Inc., New York and London; in an F-1 F11 C1 C1 "22 +1 article entitled Diode Coincidence and Mixing Circuits i" Ci Ci Rf' in Digital Computer-sf by Tung Chang Chen, in volume 38 0f the Proceedings of the Institute of Radio Engi- ("4) 1 o 1 1 1 1 0 neers, on pages 511 through 514; and in U.S. Patent 3 1 0 0 1 1 1 1 No. 2,644,887 entitled synchronizing Generator, by (l) i (l) A. E. Wolfe, Jr., issued July 7, 1953.

The operation of the circuit of Fig. 1 is illustrated in 2 g (l) g g Table III wherein two operations are performed, one 1 1 0 1 1 0 0 combining X5, Aj, and Bi having binary values equivalent 1 o l o 0 to 1-111, 95, and 191, respectively, to form the reg g t; l1 g 1 sult R5 of 175; and the other combining X1, A5, and 1.5 P1) 0 1 1 1 1 0 B,- having values of +356, 105, and l07 to form the 1 1 D 0 1 0 1 result Ri Of +144. 0 0 0 0 0 0 0 In Table III below, the values for the carry C142 (o) g (l) (l) g 3 g is obtained with the aid of Equation 3 above. Since the carry signal C, 12 is developed by flip-op C2 of Fig. 1, 20 (+B-v 0 1 0 0 0 0 1 a one binary digit delay is `introduced resulting from the inherent delay characteristic of a flip-flop. Thus each value of the carry C, 12 in Table III is obtained by refce: F-2 C? C1 F1101 1 erence to the Values for variables F11-3, F14-2, and C, 12 i H+ "o 1 "1 in the next lower order binary digital place of the table. 1C?=ll";'2-(,.1 For example, the value for C, 12 in the 7th binary digital` place of the table is determined by noting that F1'3=0, 00,2: Fifa( F11-1+ CIL!) F,` 1"2=1, and C1 12=1 in the 6th binary digital position of the table. Referring to Equation 3 above, it is noted C,1=F,+1(F,"l C',2 1) +F,2F,1"C? 1 that Cf (equivalent to C 12 in the 7th binary digital 30 Table lll 10 9 s 7 5 4 a 2 1 :Binary time intervals 512 256 128 s4 32 16 s 4 2 1 Binary weights o 1 o 1 1 1 1 X, +111 o 1 o 1 1 1 1 1 A, -95 o 1 1 1 1 1 1 B, -191 n 1 o 0 o 1 1 1 1 F}-=F,t 1 o o 1 1 1 1 1 o 173, 1 1 o 1 1 1 0 o o o o CL,

1 1 1 o 1 o 1 o o o 1 R1 -175 1o 9 s 7 e 5 4 3 2 1 t 512 256 12s 64 32 1e s 4 2 1 Binary weights l 1 1 1 o 1 o o Xi+a5e o o 1 1 o 1 o o 1 A1f- 105 o 1 1 0 o 1 1 B, -107 o 1 o 1 1 o 0 1 1 o F}"= ,l o o 1 1 o 1 o 1 1 o F73, o 1 0 o 1 0 o o 0 CL,

0 o 1 o o 1 0 n o o 0 R1 +144 l 2.... place of the table) has a 1 value when Cf- "1 and 65, Itdoes not appear that these carry functions are as either Fim-:O or F,- 12=1. Thus Cj 12 is equal to l in the 7th binary digital place of Table III. In a similar manner the remainder of the values for C, 12 are cornpleted in the table.

Since both of the carries C7-2 and Cil have been defined as having Weights of 2 in Table II above it is apparent that other carry denitions are possible with a rearrangement of digits in the ranges 3) and 2). One variation is illustrated in Table IV below, following which are the corresponding carry definitions.

economical as those utilized in dening the embodiment of Fig. l, where C,-1=Fi2.

Another variation in carry definition is illustrated in Table V, below, wherein a carry-over-two variable C142 is dened, having a weight vof 1, the corresponding new carry C# having a weight of 4. The algebraic denitions derived from Table V are shown below the table. Again it will be noted lthat the definition C,1=F,2 appears to be considerably more economical.

Table V Aggregate Weight -2 +1 -1 -1 -4 -2 +1 X,-A,-1=1,-C ,cg..1 172 F1 Cl., Cl-l Cl 0l Rf (-4) 1 o 1 1 1 o o 1 o o 1 1 o 1 3) 1 o 1 o 1 o 1 1 1 1 1 1 o 1 1 s a .1. a 1 s ("2) 1 1 o 1 0 1 o 1 1 1 o o 1 0 8 3 l 3 i i 1) o 1 1 1 o 1 1 1 1 o o o 1 1 o o o o o o (o) o 1 o 1 o o o o 1 1 o o 0` o (+1) o 1 ol o o 0 1 www. (612+ 61..) 61.5.1.1

Reference is now made to Fig. 2 illustrating an embodiment of the present invention for receiving complementary binary input signals Aj, 1; B1, l; and X), X, representing three binary input numbers A, B, and X to produce an output binary signal series Rj representing the operation X +A -B on the input numbers. The embodiment of Fig. 2 includes gating circuits 20F(-1)]' and 20F( +2) j-l responsive to the input signals Aj, B1, and X1 and for producing voltagelevel signals Ffl and F, +2), respectively, which are applied to the input circuit of a direct-current trigger circuit F(1)j and a complementer Co, respectively. The embodiment of Fig. 2 further includes a ip-op F(+2)i-1 coupled to the complementer Co and responsive to the output signals of complementer Co for producing complementary lip-op output signals F, 1+2 and FPU-2. A gating circuit 20C(-)j-1 is coupled to the direct-current trigger circuit F(-l)j and flip-op F(+2)j-l for receiving signals F7- 1+2 and 1 1+2 from flip-flop (F+2)-1, and signals F,-1 and f from the direct-current trigger F(-1)j for producing tlip-iiop control signals which are impressed on a carry flop-flop C(--1)j1. The output signals C74- and 1 from flip-dop C(-1)1-1 are impressed on output gate 20Rj along with signals Ffl, fl; and FP1-t2, 1 1+2; output gate 20Rj producing, in response thereto the output signal series Ry'.

The ip-ops F( +2) j-l and C( j-l, the direct-current trigger circuit F( -1) 1', and the complementer Co are similar to the ip-op, direct-current trigger, and complementer, respectively, described in detail in relation to Fig. 1. It is therefore deemed unnecessary to further describe these elements at this time.

The mechanization of the gating circuits 20F(-1)j, 20F(+2)j-1, 20C(-)]-1, and v20R1' of Fig. 2 are facilitated, as before in conjunction with Fig. 1, by reference to mechanization functions, derived from logical Boolean equations, defining the structure of these gating circuits.

The mechanization functions for the embodiments of Fig. 2, designed to perform the operation: X,+A,-B, may be derived in a manner similar to that described a'bove from Tables VI and VII below, illustrating the translation of input signals X1, A1, and B, into weighted signals Fj+2 and Fihaving weights +2 and -1, respectively; and the translation of signals F,+2, 'F1-1, C, 1+, and C, 1 having weights +2, -1, +1, 1, respectively; into result indicating signals C14, Cf, and R having weights +2, 2, and +1, respectively. It is significant to remember that C,+=F,+2, therefore F, 1+2 is equ1v4 18 lalent to the delayed carry Cj 1+ in Table similarly, F is equivalent to Pfl.

Table VI [Function X-i-A--Bl VII below;

+1 +1 -1 X1 Ai Bi F,"

o o 0 o o (o) o 1 1 o o 1 0 1 o lo Table VII +2 -1 +1 1 +2 -2 i +1 Fi+2 Ff Op, 0,1, Ct C, l?)

o o o 0 0 o 0 (o) o o 1 1 o 0 A0 -1 o 1 1 o o o o 1 1 o 1 1 1 0 0 n o 1 o 1 1 (-1) 0 1 0 0 o 1 1 o 1 1 1 o 1 1 2) o K 1 o v1 o 1 o 0 o 1 o o o 1 (+1) 1 o 0 1 1 1 1 1 0 o 1 1 1 Utilizing the same techniques previously explained in detail, a' logical Boolean expression for variable Pfl may be derived from Table VI above as:

In a similar manner, logical Boolean expressions for variable Cf may be derived from Table VII above as followsf By,` substituting the equivalents F71-3 and F, 1+2 for Pfl and C,- 1+, respectively, the above expression be comes:

A logical Booleanv expression for the variable Rj may be derived from Table VII as: l

and again substituting the equalities F1113=F1, and F, 1+2=C 1+,'the above expression becomes;

The above Expressions 5, 6, 7, and 8 may be put in theform of mechanization functions for the embodiment of Fig. 2 as follows:

which reduces to the simplified partial changing functions: [C()l] The mechanization of gating circuitsl 20F(f1)], .20T

20F(+2)j-1, 20C(-)i, and 20Rj according to the corresponding functions should be apparent from the foregoing examples. 1

The operation of the circuit of Fig. 2 is illustrated in 'Table VIII below:

Table VIII [Operation Xf-l-Ay-Bfl 9 s 7 e 5 4 a 2 1 Ve e4 32 1c s 4 2 1 Binary weight 1 o o 1 1 X; +51 1 1 o o o 1 1 .4, +99 1 o 1 1 1 1 1 B, -95

.3 o o o o o 1 1 1 1 Fi Ff 2 o o 1 o o o 1 1 o Fi-FCi-l o o 1 1 1 1 1 1 o 0111 o o o 1 1 o 1 1 1 R, +55 o 1 1 o o 1 1 X; +51 o 1 o o o 1 1 A, +35 1 o 1 1 1 1 1 n,

o 1 o o o 1 1 0 Fi-lz Ci-l 1 o o 1 1 1 1 Fi'ad?? 1 1 1 1 1 1 1 1 o C-i In Table VIII above it should be noted that the values entered in the table for the variable Ci 1 are obtained from Equation 7 above expressing the variable Cf in terms of its previous value C, 1 and the variables F115 and F, 1+2. In the table, the variable C1- is expressed as C,- 1 indicating that the variable is treated as delayed one binary digit place in comparison with the variable Fim. This is consistent with the structure of Fig. 2 in that the carry signal 1- is produced by the flip-flop C(-1)j#-1, the ip-flop introducing a one binary bit delay. In Table VIII, therefore, each value for CP1 is determined by noting the values of variable Fil-3, F, 1+2f and C, 1 in the next lower order binary digital place of the table.

As inthe case of the equations defining the embodiment of Fig. 1, the equations defining the embodiment of Fig. 2 may be modified to define difrerent carry functions. It appears, however, that defining Cfr to be equal to F 1+2 is the most economical.

The principles thus far discussed are readily extended to greater numbers of input signals. It appears that the most economical mechanizations for four, ve, or six input signals are achieved by combining the input signals three at a time in the manner discussed. Thus, in the embodiment of Fig. A3, where the operation 2@ X,+A,-B,Y, is to be performed, the signals X1, A and B1 are first translated to the variables F1 1+2 and Pfl" in the manner previously discussed; signal Fj 1+2 being formed through a complementer circuit Co and a flip-flop F(l2) 1 producing signals Fj 1+2, and F14, and signals Ffl and Ff being formed through direct-current trigger circuit F (1)1. The variables F,- 1+2, Fj-l, and Yi, considered as having weights +1, 1, and 1, respectively, are then combined to form the variables G, 1"2 and G,-+1, which are similar to the variables ELI-Z and F+1 previously discussed, signals Gpl-2 and G'ljl being formed respectively through pulse complementer Co and dip-hop G(-2)j1, and direct-current complementer circuit G(+1 )j. {30W-1m F;1=F13(A 3,-, X,-)

Table IX 7 sl 5 4 a 2 1 1 54 32 1e s 4 2 1 Binary weight o 1 1 o 1 1 1 X, +55 o o o 1 o 1 1 .41 +11 o 1 o 1 1 1 1 B, -47

o o o o 1 1 1 Y, -7

o 1 o o 1 1 o Fai-'Pci *1 1|! o 1 o o 1 1 Fi Ff o 1 1 o n 1 o Gi' G2 o 1 o o 1 1 o f-1 C2. o o 1 1 o o o 1-1 o o o 1 1 n o R, +12

From the foregoing description it is apparent that the present invention provides a multiple input binary adder-subtracter wherein any of a plurality of addition or subtraction operations may be performed with a minimum of gating circuit elements. Since carries are provided which may represent vany desired result weight it is apparent that the type of adder-subtracter provided is readily adaptable for use in binary-coded decimal sys-v tems where carry corrections are to be performed by changing the initial result weight at the beginning of a binary-coded decimal'digit group.

What is claimed as new is:

1. An arithmetic unit for adding M binary input numbers and simultaneously subtracting N binary input numbers therefrom .to form the'correspondng binary result number, where M and N are each an integer not smaller than l and (M-l-N) is an integer greater than 2, the M and the N binary input numbers being represented by M and N corresponding series of binary electrical input signals, respectively, and the result being represented by a series of electrical output signals, each binary electrical input signal of a series representing a binary digit of the corresponding binary input number and each binary electrical output signal of a series representing a binary digit of the binary result number; said arithmetic unit comprising: first means responsive to the binary electrical input signals and for providing each input signal of the M series of input signals with a significance of +1 and for providing each input signal of the N series of input signals with a significance of 1, and for producing an intermediate series of binary electrical signals indicating the aggregate significance of said binary electrical input signals in accordance with a predetermined binary code effective only within said arithmetic unit; second means coupled to said first means and responsive to said intermediate series of binary electrical signals for producing binary electrical carry signals; and third means coupled to said first and said second means and responsive to said intermediate series of binary electrical signals and said carry signals for producing the series of electrical output signals representative of the desired binary result number.

2. The arithmetic unit defined in claim 1 wherein M is equal to l and N is equal to 2; wherein said intermediate series of binary electrical signals produced by said first means includes first intermediate signals 13j-2 representing a significance of -2 and second intermediate signals Fit-1 representing a significance of +1, where the subscript j indicates a binary digital place of the input binary numbers; and wherein said first means includes a first gating circuit responsive to the binary electrical input signals for producing said first intermediate signals Ffa and a second gating circuit responsive to said binary input signals for producing said second intermediate signals Fftl, said first and said second gating circuits each including at least one logical and and one logical or circuit.

.3. The arithmetic unit defined in claim 2 wherein said binary electrical carry signals produced by said second means are representative of first and second carry signals C, 11 and C, 12, respectively, each being assigned a significance of -1, where the subscript (j--1) indicates a next lower order binary digital place of the binary input numbers as compared to a binary digital place of the input numbers indicated by the subscript j; and wherein said second means includes first circuit means responsive to said first intermediate signals 137-2 for delayin-g said first intermediate signals by one digital position to produce signals F, 12 directly representative of said first carry signals C741, and' second circuit means responsive to said rst carry representing signals F7-12 and said second intermediate signals F,-+1 for producing said second carry signals C,- 12.

4. The arithmetic unit defined in claim 3 wherein said third means includes at least one logical and and one logical or circuit connected in a manner to produce the series of electrical output signals in accordance with particular patterns of occurrence of said second intermediate signals F,-+1 and of said first carry representing signals F,- 12 and of said carry signals Ci 12.

5. The arithmetic unit defined lin claim 3 wherein said first carry representing signals are represented by a pair of complementary carry representing binary signals Fimfz and ITE- 14, where a bar over a symbol of a signal indicates the complement of the signal represented by the symbol, wherein said second intermediate signals are represented by a pair of complementary second intermediate signals Fj+1 and ffl; wherein means is provided for applying clock pulse Cp to said first and second circuit means; wherein said first circuit means includes a bistable ip-fiop for receiving said first intermediate signals Iii-2 and for producing the pair of complementary carry representing binary signals FP1-2 and I,- 1r2; and wherein said second circuit means includes a bistable flip-flop C2 hav ing input circuits l and 0 and producing complementary output signals C, 1*2 and C17- 12 representing said second carry signals C542, said second circuit means further including a logical gating circuit for receiving said complementary second intermediate signals F-+1, lig-+1 and said complementary carry representing binary signals F,- 1-2, 1-2, and for producing control signals 1C2 and 8C2 which are applied to the 1 and 0 input circuits, respectively, of said bistable flip-flop C2, said logical gating circuit having two logical and circuits connected in accordance with the logical function:

oC2=- 2,.F,-1.Cp where a dot and a plus indicate a logical and and a logical or function, respectively, and where the bar (r) over a symbol of a signal indicates the complement of the signal represented by the symbol.

6. The arithmetic unit defined in claim 2 wherein the M binary input number is represented by a binary electrical input signal series Xi, the N binary input numbers are represented by binary electrical input signal series A, and Bj, respectively, and the binary result number is represented `by a series of electrical output signals R1; wherein said first gating circuit includes two logical and circuits and two logical or circuits connected to produce said first intermediate signals Ff in accordance with the Boolean algebraic equation:

and wherein said second gating circuit includes four logical and circuits and one logical or circuit connected to produce said second intermediate signals Ffll in accordance With the Boolean algebraic equation:

where the dot and parenthesis indicate a logical and function, the plus (l) indicates a logical or function, and a bar (r) over a symbol of a signal indicates the complement of the signal represented by the symbol.

7. The arithmetic unit defined in claim 1 where M is equal to 2 and N is equal to l; wherein said intermediate series of binary electrical signals produced by said first means includes first and second intermediate signals Fy+2 and Fi-l, respectively, representing a significance or +2 and -l, respectively, where the subscript j indicates a binary digital place of the input numbers; and wherein said first means includes a first gating circuit responsive to the binary electrical input signals for producing said first intermediate signals F7-+2 and a second gating circuit responsive to the binary electrical input signals for producing said second intermediate signals Pfl, said first and said second gating circuits each including at least one logical and and one logical or circuit.

8. The arithmetic unit defined in claim 7 wherein said binary electrical carry signals produced by said second means are representative of first and second carry signals C, 1+ and C,- 1 having a significauce of -l-l and -1, respectively, where the subscript (j-l) indicates the occurrence of signals in the digital position next to the position indicated by the subscript j; and wherein said second means includes first circuit means responsive to said first intermediate signals Fftz for delaying said first intermediate signals to occur at the next binary digital place of the input numbers to produce signals F, 1+2 directly representative of Said assegna '23 ,rst carry signals C144", and second circuit means responsive to said second intermediate signals Pfl and said first carry representing signals F 1+2 for producing said second carry signals C,- 1.

9. The arithmetic unit defined in claim 8 wherein said third means includes at least one logical and and one logical or circuit connected to produce said series of electrical ouput signals in accordance with particular combinations of occurrence said first carry signal C744', said second carry signal Cyn, and said first intermediate signals F,l.

, 10. The arithmetic unit defined in claim 1 wherein M and N are each equal to 2; and wherein said intermediate series of binary electrical signals produced by said first means includes first and second intermediate signals Gd2 and Gffl, respectively, where the subscript jindicates a binary digital place of the input binary numbers; and wherein said first means includes a first .gating circuit responsive to the M series of binary electrical input signals and one of the N series of binary electrical input signals for producing first and second partial intermediate signals Ff'z and Pfl representing a significance of -l-Z and 1, respectively, a delay circuit coupled to said first gating circuit and responsive to said first partial intermediate signals 11j-+2 for producing delayed partial intermediate signals F,- 1+2, where the subscript (j l) indicates the occurrence of signals in the digital position next to the position indicated by the subscript j, and a second gating circuit coupled to said first ygating circuit and to said delay circuit and responsive to said second partial intermediate signals Pfl said delayed partial intermediate signals F, 1+2, and the other one of said N series of binary electrical input signals for producing said first and second intermediate signals Gf2 and Gii'l, respectively.

11. The arithmetic unit defined in claim l() wherein said binary electrical carry signals produced by said vsecond means include first and second carry signals 'C7 1l and C142, respectively, `each being assigned a significance of 1; and wherein said means includes rst circuit means coupled to said second gating circuit and responsive to said first intermediate signals Gi2 for delaying said first intermediate signals by a period 'of time so as to produce signals (B1- 1 2 corresponding to signals Gfz and occurring in the next digital place, signals G 12 directly representing said rst carry signals C,- 1l, and second circuit means coupled to said first circuit means and to said second gating circuit and responsive to said first carry representing signals G, 1*2 and said second intermediate signals Gjil for producing said second carry signals Cj 12.

12. The arithmetic unit defined in claim l1 wherein said third means includes at least one logical and and one logical or circuit connected in a manner to produce the series of electrical output signals in accordance with particular patterns of occurrence of said second intermediate signals Gji'l and said second carry signals C, 12.

13. An electronic circuit synchronized by externally applied synchronizing pulses Cp for simultaneously receiving a first, a second, and a third binary input number and for subtracting the first and the second binary input numbers from the third binary input number to produce a corresponding result binary number, the first, the second, and the third binary input numbers being represented by binary input signal series Ai, 13,-, and Xi, respectively, and the binary result number being represented by output binary signal series Ri, where the subscript j indicates a binary digital place of the binary input numbers, each binary signal oli a series representing a binary digit of the corresponding binary number; said electronic circuit comprising: first means responsive to the input binary signal series for providing each binary signal of binary signal series Ai, Bj, and X1 with a significance of 1, 1, and -l-l, respectively, and for producing intermediate signals indicating the total Zbl significance of the input binary signal series, said first means including a first gating circuit responsive to said input binary signal series for producing first intermediate signals Ffz, and a second gating circuit responsive to said input binary signal series for producing second intermediate signals Fffl, said first and second intermediate signals Fj-Z and Fffl representing a significance of 2 and -l-l, respectively, said series of intermediate binary electrical signals consisting of said first and second intermediate signals; second means coupled to said first means and responsive to said first and second intermediate signals Fj-Z and Ff-Ll for producing first and second carry signals Ci 1l and C542, respectively, each being provided wtih a significance of 1, where the subscript (j l) indicates the occurrence of signals in the digital position next to the position indicated by the subscript j, said second means including first circuit means coupled to said rst gating circuit and responsive to said first intermediate signals lig-2 for delaying said first intermediate signals, thereby to produce signals F, 12 directly representative of said first carry signals C, 1l, and second circuit means coupled to said second gating circuit, and said first circuit means and said second intermediate signals Pfl and responsive to said first carry representing signals Fjl-Z for producing said second carry signals C,- 12; and third means coupled to said first and said second means and responsive to said second intermediate signals Fy-i'l, and said second carry signals C, 12 for producing the signal series R, representing the corresponding binary result number.

14. The electronic circuit defined in claim 13 wherein said binary input signal series Aj, Bi and X,- are represented by complementary signal pairs Aj, j; Bj, j; and Xj, X1; respectively, where a bar over a symbol of a signal indicates the complement of the signal indicated by the symbol; wherein said irst gating circuit includes two logical and circuits and two logical or circuits connected to produce said first intermediate signals Ff? in conformity with the logical Boolean equation:

and wherein said second gating circuit includes four logical and circuits and one logical or circuit connected to produce said second intermediate signals Fftl in conformity with the logical Boolean equation:

where a dot or a parenthesis indicates a logical and function, and a plus (-l) indicates a logical or function.

15. The electronic circuit defined in claim 13 wherein said intermediate signals Pfl are represented by complementary binary signals Fj+l and Ff'fl, the bar over a symbol of a signal indicating the complement of the signal represented by the symbol; wherein said first circuit means includes a first bistable flip-flop for receiving said rst intermediate signals Fj-z and for producing complementary signals B fz and FP1-2; and wherein said second circuit means includes a flip-flop control circuit and a second bistable flip-flop, said flip-flop control circuit being coupled to said first circuit means and said second gating circuit and responsive to complementary signals Fffl, Fjil, and F, 12, 12 for producing fiip-fiop control signals 1C2 and OCZ for introduction to said second flip-flop to produce the complementary carry signals CP1-2 and 1-2.

16. The electronic circuit defined in claim 15 wherein said flip-flop control circuit includes two logical and circuits electrically coupled to produce said flip-flop control signals 1C2 and OCZ, said logical and circuits where the dot indicates the logical and function.

17. The electronic circuit defined in claim 13 wherein said second intermediate signals F,+1, said first carry representing signals F, 1 2, and said second carry signals C, 12 are respectively represented by complementary signal pairs F,+1, H; F, 1 2, FP1-2; and C 12, 12; where a bar over a symbol of a signal indicates the complement of the signal represented by the symbol; and wherein said third means includes four logical and circuits and one logical or circuit electrically connected to produce said signal series R1, said logical and and or circuits being electrically connected according to the logical equation:

where a dot and a plus indicate a logical and and a logical or function, respectively.

18. An electronic arithmetic circuit synchronized by externally applied synchronizing pulses Cp for adding a first and a secondary binary input number and for simultaneously subtracting therefrom a third binary input number to produce a corresponding binary result number, the first, the second, and the third binary input numbers being represented by a rst, second, and third electrical input signal series Xi, A, and Bi, respectively, and the binary result number being represented by signal seriesl R1, the subscript i indicating a binary digital place of the binary input numbers, said electronic arithmetic circuit comprising: first means responsive to the electrical input signal series for providing each electrical input signal of the X5, Ai, and B,- series with a significance of +1, +1, and 1, respectively, and for producing irst and second intermediate signals F7-+2 and 13j-1, respectively, indicating the aggregate significance of the associated input signal, said rst means including a first gate responsive to said electrical input signal series for producing said first intermediate signals F,+2, and a second gate responsive to said electrical input signal series for producing said second intermediate signals Fj-l, said first land said second gating circuits each including at least one logical and and one logical or circuit; second means coupled to said first means and responsive to said first and second intermediate signals F7+2 and Pfl, for producing iirst and second carry signals CFU- and C, 1 respectively, having a significance of `-l-l and --1, respectively, where the subscript (j-l) indicates the occurrence of signals in the digital position next to the position indicated by the subscript j, said second means including a rst circuit coupled to said first gate and responsive to said first intermediate signals F,+2 for delaying said first intermediate signals, thereby to produce signals F, 1+2 directly representative of said first carry signals C,- 1+, and a second circuit coupled to said second gate and said first circuit and responsive to said second intermediate signals Ffl and said first carry representing signals F, 1+2 for producing said second carry signals C, 1 and third means coupled to said first and said second means and responsive to said second intermediate signals F, 1 and said second carry signals C, 1 for producing signal series R, representing the binary result number.

19. The electronic arithmetic circuit defined in claim 18 wherein the electrical input signal series X1, A7, and Bj are represented respectively by complementary pairs of binary signal series Xi, 'j; Aj, i; and Bj, i; the bar over a symbol of a signal indicating the complement of the signal represented by the symbol; wherein said first gate includes two logical and circuits and two 26 logical or circuits electrically coupled to produce said first intermediate signals F,+2, according to the following logical equation:

Fj+2=Xj (Ajbj) I .AT and wherein said second gate includes four logical and circuits and one logical or circuit electrically coupled.,

to produce said second intermediate signals F, 1, according to the following logical equation:

20. The electronic arithmetic circuit defined in claim 18 wherein said second intermediate signals Ffl are represented by complementary pairs of binary signals F,- 1 and 1711-1, a bar over a symbol of a signal indi'- cating the complement of the signal; wherein said first circuit includes a first bistable flip-flop for receiving said first intermediate signals F,-+2 and for producing complementary signals F, 1+2 and 1+2 representing said first carry signals C, 1+; and wherein said second circuit includes a flip-flop control circuit coupled to said second gate and said first Hip-flop and responsive to complementary signal pairs F, 1+2, lib-+2 and F 1, -l for producing iiip-iiop control signals 1C(-) and 0C(), and includes a second bistable iiip-iiop coupled to said flip-flop control circuit and having l and 0 input circuits responsive to flip-flop control signals 1C() and 0C(), respectively, or producing a complementary pair of out.- put signals C, 1 1 representing said second carry SlgnaiS C: 1`.

21. The electronic arithmetic circuit defined in claim 20 wherein said flip-flop control circuit includes two logical and circuits electronically connected to produce said flip-flop control signals 1C() and 0C(-), said logical and circuits being electrically connected according to the logical Boolean equations:

1C(-)=F,1.F,t2,.0p 0c(-)=",1.r',t2,.0p where a dot indicates a logical and function.

22. The electronic Varithmetic circuit defined in claim 18 where said second intermediate signals 13g- 1, said first carry representing signals F,- 1+2, and said second carry signals C 1 are respectively 'represented by complementary binary signal pairs Erl, E F,- 1+2, lill-t2; and C, 1 C,- 1 a bar over a symbol of a signal indicating the complement of the signal represented by the symbol, and wherein said third means includes four logical and circuits and one logical or circuit connected to produce signal series Ri, said logical and and or circuits being connected as indicated by the logical Boolean equation: R,-=F,1.",t 21.gf ,+FFi21.nl

JFFIIFM INFM? .21 where a dot indicates a logical and `function and a plus a logical or function.

23. An electronic circuit synchronized by externally applied synchronizing pulses Cp for adding a first and a second binary input number and for simultaneously subtracting therefrom a third and a fourth binary input number to produce a corresponding binary result number, the first, the second, the third, and the fourth binary input numbers being represented by binary input signal series Xi, Aj, Bj, and Y, respectively, and the binary result number being represented by a binary output signal series Fi, where the subscript j indicates a binary digital place of the input numbers, each binary electrical signal of a series representing a binary digit of a corresponding binary number; said electronic circuit comprising: an

assegna evaluation circuit for receiving the binary input signal series and for providing each binary input signal of the X1, Ai, B7, and Y, series with respective values of +1, +1, -l, and -l, and for producing first and second evaluational signals (lf2 and Gfl, respectively, indicating the aggregate evaluation provided for the input signal series in accordance with a predetermined binary code wherein the first and the second evaluational signals Gf2 and Gfl arc evaluated as -2 and +1, respectively, said evaluational circuit including a first gating circuit responsive to each binary input signal series Ai, Bj, and Xi, for producing first and second sub-evaluational signals lil-+2 and Ffl representing values of +1 and 2, respectively, a delay circuit coupled to said first gating circuit and responsive to said first sub-evaluational signals Ffz, for delaying said signals, thereby to produce delayed rst sub-evaluational signals F,- 1+2, and a second gating circuit coupled to said first gating circuit and to said delay circuit and responsive to said second subevaluational signals Pfl, said delayed rst sub-evaluational signi ls P,- 1+2, and said binary input signal series Y,- for producing said first and second evaluational signals Gf2 amd Gfl respectively, where the subscript (j-l) indicates the occurrence of signals in the position next to the position indicated by the subscript j; a carry circuit coupled to said evaluational circuit and responsive to said first and second evaluational signals Gf2 and Gfl for producing first and second carry signals C7- 1l and C, 12, respectively, each having a value of 1, said carry circuit including a Erst portion coupled to said second gating circuit and responsive to said first evaluational signals Gf2 for delaying said evaluational signals for a period of time so as to produce signals Gj 12 directly representing said first carry signals C,- 1l, and said carry circuit including a second portion coupled to said first portion and to said second gating circuit and responsive to said first carry representing signals G7- 12 and said second evaluational signals Gfl for producing said second carry signals C,- 12; and an output circuit coupled to said evaluational circuit and said carry circuit and responsive to said second evaluational signal Gy-"l'l, said first carry representing signals Gj 1-2, and said second carry signals C542 for producing the binary output signal series Rj representative of the desired binary result number.

24. The electronic circuit defined in claim 23 wherein the binary input signal series Xi, A1, and B7- are represented respectively by complementary binary input signal series X7, X1; A74, i; and Bj, j, where a bar over a symbol of a signal indicates the complement of the signal indicated by the symbol; and wherein said first gating circuit includes a first gate responsive to the complementary signal series Xi, Xy, Aj, j; Bj, -g for producing said first subevaluational signals FW, and a second gate responsive to said complementary binary input signal series Xi, 271,-; Aj, j; and Bj, j, for producing said second suoevaluational signals Ffl, said first gate and said second gate each including at least one logical and circuit and one logical or circuit.

25. The electronic circuit defined in claim 24 wherein said first gate includes two logical and circuits and two logical or circuits connected to produce said first subevaluational signals ily-+2, said logical and and or circuits being connected in conformity with the logical Boolean equation:

FL2=X1` (Ai-l" Bi) *i-Aii and wherein said second gate includes four logical and circuits and one logical or circuit connected to produce Said SEC-nd gubvaluational signals Pfl, said logical and and or circuits being connected in conformity with the logical Boolean equation:

Fj-l:LXj-l-BfXf-i-A5.Bj.Xii-i.Bj.Xf

where a dot or a parenthesis indicates a logical 2@ and function, and where a plus indicates a logical "orl function.

26. The electronic circuit defined in claim 23 wherein said delay circuit includes a bistable flip-flop responsive to said first sub-evaluation signals Ffz for producing said delay first sub-evaluational signals F7- 1+2.

27. The electronic circuit defined in claim 23 wherein the input binary signal series Yi, said second sub-evaluational signals Ffl, and said delayed first sub-evaluation signals Fj 1+2 are represented each by complementary input binary signal pairs Yy, Yi; Ffl, Ffl; and Ff2, lf2, where a bar over a symbol of a signal indicates the complement of the signal indicated by the symbol; and wherein said second gating circuit includes a first gate coupled to said first gating circuit and said delay circuit and responsive to the complementary input binary signal pairs Ffl, Ffl, and F, 1+2, ligft2 for producing said first evaluational signals Gf2, and includes a second gate coupled to said first gating circuit and said delay circuit and responsive to the complementary input binary signal pairs Ffl, Ffl, and F,- 1+2, lib- J2 for producing said second evaluational signals Gffl, each of said first and said second gates having at least one logical and" and one logical or circuit.

28. The electronic circuit defined in claim 27 wherein said first gate includes two logical and circuits and two logical or circuits electrically connected to produce said first evaluational signals Gfz, said logical and and or circuits being electrically connected in accordance with the logical Boolean equation:

G2=rt21 Fr1+Yf +FlYi and wherein said second gate includes four logical and" circuits and one logical or circuit electrically connected to produce said second evaluational signals Gfl, said logical and and or circuits being electrically connected in accordance with the logical Boolean equation: G,+1=F,lfiJfrrFi,

-l-'f-l-Fit-Yi'ip'i-l-Fl-BLY" where a dot and a parenthesis each represent a. logical and function, and a plus represents a logical or function.

29. The electronic circuit defined in claim 23 wherein said first portion includes a rst bistable flip-flop coupled to said second gating circuit and responsive to said first evaluational signal Gf2 for producing complementary signal pairs G 12, (lj- 1 2 representing said first carry signals 7-11. p

30. The electronic circuit defined in claim 29 wherein said second section includes a flip-flop control circuit and a second bistable flip-flop, said flip-flop control circuit being coupled to said first portion and responsive to said complementary signal pairs Gffz, 1-2 for producingl first and second flip-flop control signals 1C2 and 0C2, respectively, and said second bistable flip-flop being coupled to sadi flip-flop control circuit and having 1 and il input circuits responsive respectively to said first and second flip-flop control signals lCZ and 002 and for producing complementary output signals C- 1' and 12 representing said second carry signals Cflz.

3l. The electronic circuit defined in claim 30 wherein said fiip-op control circuit includes two logical and circuits connected to produce said first and second ipflop control signals 1C2 and OCZ, respectively, said logical and circuits being connected according to the following logical equations:

where a dot indicates a logical and function.

32. The electronic circuit defined in claim 23 wherein said second evaluational signal G,+l, said first carry representing signals Gi 12, and said second carry.

signals C,. 12 are each represented respectively by complementary signal pairs Gffl, Gfl'; Gpl-2, Gj 12; and C, 12, Cy-l a bar over a symbol of a signal indicating the complement of the signal represented by the symbol; and wherein said output circuit includes four logical and circuits and one logical or circuit connected to produce the binary output signal series R, in accordance with the logical function: R,=G,-+.,121.01+`G2tC1+ f+121-ct1+G1G210?-. where a dot and a plus (-1-) in the above function indicates a logical and and a logical or function, respectively.

33. An electronic arithmetic circuit for simultaneously receiving M and N binary input numbers and for summing the M binary input numbers and for subtracting the N binary input numbers from the sum of the M binary input numbers, thereby to produce a corresponding binary result number, where (M-l-N) is an integer greater than 2, and M and N are each an integer not lest than 1, the M and the N binary input members being respectively represented by M and N corresponding series of binary electrical input signals, and the binary result number being represented by a series of electrical output signals; said electronic arithmetic unit comprising: a translation circuit responsive to the M and N binary electrical input signals for providing each input signal of the M and N inputrsignal series with a significance References Cited in the tile of this patent UNITED STATES PATENTS Knutsen Nov. 12, 1957 OTHER REFERENCES Progress Report #2 on the Edvac, Univ. of Penna., Fig. PYO-l08, February 1947.

Synthesis of Electronic Computing and Control Circuits, Harvard University Press, 1951; pages 164-165 reliedy on.

Serial Digital Adders for a Variable Radix of Notation, by Townsend, Electronic Engineering, October 1953, pages 410-416.

UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,888,202 May 26, 1959 John V. Blankenbaker et al.

t is hereby certified that error appears in the printed specification of the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 14, line 27, the left-hand portion of the equation should read as shown below instead of as in the patent:

0F(-2)j1=[2'?,: line 61, after the semicolon, strike out:

y FILS! F1221; U12-1 column 22, line 36, in the equation, after (14, insert v+ column 23, line 40, after said insert second; column 24, line 7l, for

C, 12 ancif, 1-2 read n 0,2., and @2 1 column 25, line 28, for secondary read secondcolumn 26, line 26, for

F",F read Ff, ;[1 line 50, for

C11-1 C11-1 read 0,11, 0,21; line 72, for F, read R,-; column 27, line 13, for +1 and 2 read +2 and -l line 54, for

E+? read -F,+2- column 29, line 2, for

G j, second occurrence, read L-j" same line 2, for

G, 12, second occurrence, read E121 Signed and sealed this 29th day of March 1960.

[SEAL] Attest: KARL H. AXLINE, ROBERT C. WATSON,

Attestzng Opcer. Uommz'ssz'oner of Patents. 

